Purely (non-)strongly real Beauville groups
نویسندگان
چکیده
منابع مشابه
More on Strongly Real Beauville Groups
Beauville surfaces are a class of complex surfaces defined by letting a finite group G act on a product of Riemann surfaces. These surfaces possess many attractive geometric properties several of which are dictated by properties of the group G. A particularly interesting subclass are the ‘strongly real’ Beauville surfaces that have an analogue of complex conjugation defined on them. In this sur...
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We explicitly construct infinitely many a non-abelian strongly real Beauville p-groups for every prime p. Until very recently only finitely many non-abelian strongly real Beauville p-groups were known and all of these were 2-groups.
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We generalize earlier work of Fuertes and González-Diez as well as earlier work of Bauer, Catanese and Grunewald by classifying which of the irreducible Coxeter groups are (strongly real) Beauville groups. We also make partial progress on the much more difficult question of which Coxeter groups are Beauville groups in general as well as discussing the related question of which Coxeter groups ca...
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Beauville surfaces are a class of complex surfaces defined by letting a finite group G act on a product of Riemann surfaces. These surfaces possess many attractive geometric properties several of which are dictated by properties of the group G. In this survey we discuss the p-groups that may be used in this way. En route we discuss several open problems, questions and conjectures.
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In this paper we construct new Beauville surfaces with group either PSL(2, p), or belonging to some other families of finite simple groups of Lie type of low Lie rank, or an alternating group, or a symmetric group, proving a conjecture of Bauer, Catanese and Grunewald. The proofs rely on probabilistic group theoretical results of Liebeck and Shalev, on classical results of Macbeath and on recen...
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ژورنال
عنوان ژورنال: Archiv der Mathematik
سال: 2019
ISSN: 0003-889X,1420-8938
DOI: 10.1007/s00013-018-1288-4